Question

Using a random sample of size 77 from a normal population with
variance of 1 but unknown mean, we wish to test the null hypothesis
that H0: μ ≥ 1 against the alternative that Ha: μ <1.

Choose a test statistic.

Identify a non-crappy rejection region such that size of the test (α) is 5%. If π(-1,000) ≈ 0, then the rejection region is crappy.

Find π(0).

Answer #1

Here population variance ( ) is given, and the sample comes from a normal population.

So we can used one sample z test for testing the population mean.

So the test statistic is Z test statistics.

The formula of Z test statistic is as follows:

Where is sample mean.

= 1 (from the null hypothesis).

= standard deviation = positive square root of variance.

From the alternative hypothesis , the critical region of area 0.05 is in the right side of the normal curve.

Let's use minitab to show the critical region.

The critical value for this test is 1.645

The observations in the sample are random and independent. The
underlying population distribution is approximately normal. We
consider H0: =15 against Ha: 15. with
=0.05.
Sample statistics: = 16, sx= 0.75, n= 10.
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statistic
t-test=4.22
t-test=0.42
t-test=0.75
z-test=8.44
z-test=7.5
2.
Decide whether the test statistic is in the rejection region and
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hypothesis.
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